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An application of Siegel's formula over quaternion orders

Published online by Cambridge University Press:  26 February 2010

H.-G. Quebbemann
H.-G. Quebbemann
Affiliation:
Mathematisches Institut der Universität, Einsteinstrasse 62, D-4400 Münster, West Germany.
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Extract

Let Φ : L → ℤ be a positive definite even unimodular quadratic form, L ≅ ℤn; we put f(x) = Φ(x)/2 and call (L, f) a lattice, for short. Let min f be the minimum of the numbers f(x) ≠ 0. Fixing n (a multiple of 8), one is interested in the largest possible minimum. It follows from the theory of modular forms (cf. Sloane [6]) that

Type
Research Article
Information
Mathematika , Volume 31 , Issue 1 , June 1984 , pp. 12 - 16
Copyright
Copyright © University College London 1984

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References

1.Eichler, M.. Quadratischc Formen und orthogonale Gruppen (Springer-Verlag, 1952).CrossRefGoogle Scholar
2.Kneser, M.. Klassenzahlen definiter quadratischer Formen. Arch. Math., 8 (1957), 241–250.CrossRefGoogle Scholar
3.MacWilliams, F. J., Odlyzko, A. M., Sloane, N. J. A. and Ward, H. N.. Self-dual codes over GF(4). J. Combinatorial Theory, Ser. A, 25 (1978), 288–318.CrossRefGoogle Scholar
4.Milnor, J. and Husemoller, D.. Symmetric bilinear forms (Springer-Verlag, 1973).CrossRefGoogle Scholar
5.Serre, J.-P.. A course in arithmetic (Springer-Verlag, 1973).CrossRefGoogle Scholar
6.Sloane, N. J. A.. Binary codes, lattices and sphere-packings. Combinatorial Surveys: Proc. Sixth British Combinatorial Conf. (Academic Press, 1977), 117–164.Google Scholar
7.Tits, J.. Four presentations of Leech's lattice. Finite simple groups II (Academic Press, 1980), 303–307.Google Scholar
8.Vigneras, M.-F.. Arithmétique des algèbres de quaternions. Springer Lecture Notes, 800 (Springer-Verlag, 1980).CrossRefGoogle Scholar
9.Weil, A.. Sur la formule de Siegel dans la theorie des groupes classiques. Ada Math., 113 (1965), 1–87.Google Scholar